Asymptotic Spreading of a Cholera Epidemic Model in a Periodic Environment

Abstract

This paper is devoted to the spreading property of a cholera epidemic model, which is built upon a time-periodic reaction-diffusion system that is not necessarily monotonic. When the initial distribution of infected hosts and bacteria appears on a compact domain, we derive a rough expansion speed of the infection over space. In the case where the model parameters are constants, we obtain some analytic properties for the speed, which allows us to understand the factors that affect the spatial spreading ability of cholera. In particular, the spreading speed of cholera is the minimal wave speed of traveling wave solutions in earlier works by taking constant parameters and special incidence functions. AMS Subject Classification (2010): 35K57; 92D30